A Task-dependent Investigation on Dose and Texture in CT Image Reconstruction

Abstract

Localizing and characterizing clinically-significant lung nodules, a potential precursor to lung cancer, at the lowest achievable radiation dose is demanded to minimize the stochastic radiation effects from x-ray computed tomography (CT). A minimal dose level is heavily dependent on the image reconstruction algorithms and clinical task, in which the tissue texture always plays an important role. This study aims to investigate the dependence through a task-based evaluation at multiple dose levels and variable textures in reconstructions with prospective patient studies. 133 patients with a suspicious pulmonary nodule scheduled for biopsy were recruited and the data was acquired at120kVp with three different dose levels of 100, 40 and 20mAs. Three reconstruction algorithms were implemented: analytical filtered back-projection (FBP) with optimal noise filtering; statistical Markov random field (MRF) model with optimal Huber weighting (MRF-H) for piecewise smooth reconstruction; and tissue-specific texture model (MRF-T) for texture preserved statistical reconstruction. Experienced thoracic radiologists reviewed and scored all images at random, blind to the CT dose and reconstruction algorithms. The radiologists identified the nodules in each image including the 133 biopsy target nodules and 66 other non-target nodules. For target nodule characterization, only MRF-T at 40mAs showed no statistically significant difference from FBP at 100mAs. For localizing both the target nodules and the non-target nodules, some as small as 3mm, MRF-T at 40 and 20mAs levels showed no statistically significant difference from FBP at 100mAs, respectively. MRF-H and FBP at 40 and 20mAs levels performed statistically differently from FBP at 100mAs. This investigation concluded that (1) the textures in the MRF-T reconstructions improves both the tasks of localizing and characterizing nodules at low dose CT and (2) the task of characterizing nodules is more challenging than the task of localizing nodules and needs more dose or enhanced textures from reconstruction.

I. Introduction

Lung cancer remains the leading causes of cancer-related deaths among both men and women in the US [1]. The American cancer society estimates there has been about 234,030 new cases of lung cancer (121,680 in men and 112,350 in women), and about 154,050 deaths from lung cancer (83,550 in men and 70,500 in women) in 2018 [2]. In past decades, early detection can decrease lung cancer mortality by 14 to 20 percent among high-risk populations [3,4]. Therefore, screening high-risk populations for early detection by low-dose computed tomography (LdCT) has been recommended national-wide due to its higher efficiency compared to the chest X-ray imaging and lower radiation compared to the full dose CT (FdCT) [3]. However, the recommended LdCT screening with three low-dose scans (reconstructed by conventional algorithms such as filtered back-projection (FBP) method), each at three subsequent years respectively, might still deliver excessive exposure to patients. In addition, the recommended LdCT screening showed high false positive (FP) rates [3,5]. For example, if the reconstruction filtering is heavily applied to noisy low-dose scans, many object details may be smoothed out: compromising the task of localizing or detecting small and low contrast nodule candidates. On the other hand, if the noise filtering is insufficiently applied to the noisy low-dose scans, many noise-related variations across the field-of-view (FOV) may be detected as FPs, rendering a challenge for the task of FP reduction or characterization of the nodule candidates for true risky nodules identification. An adequate treatment of the noise in the low-dose scans in the image reconstruction stage would not only benefit high-risk populations, but also facilitate the expansion of the recommended LdCT screening to average-risk populations [6,7].

The minimal CT dosage required without compromising clinical tasks heavily depends on the specific task as well as the reconstruction algorithm, as various tasks have different tolerances to noise level and different reconstruction algorithms have different abilities of noise reduction and detail preservation, e.g. tissue texture preservation [8], which was recognized as an important biomarker in many clinical tasks [9-11]. To evaluate the detectability for these kind of biomarkers in low dose CT, the human observer model was developed in [12, 13]. In this work, radiologist scoring strategy was employed to investigate the dependence through a task-based evaluation at multiple dose levels and variable textures in reconstructions with prospective patient studies.

The CT dose can be reflected by the data acquisition protocol parameters of X-ray tube voltage (kVp) and the tube current (mAs). Although both parameters can be optimized for clinical tasks, this study considered only the current (because of its linear relationship to the dose level) and set the voltage at fixed value of 120kVp for simplicity.

LdCT image reconstruction techniques could be categorized roughly into three types: analytical back propagation, stochastic iterative reconstruction (SIR) and image restoration. With a filter (kernel) the analytical back propagation (or FBP) performs stabilized and discrete inverse Radon transformation from sinogram data [14,15]. These types of methods have been widely used as built-in algorithms of commercial CT scanners for its fast speed and stable results. Usually, CT machines provide several kernel options to suppress artifacts for different dose level scans. Image restoration was employed to enhance the results in the image domain. Over the past decade, several image post-processing methods were developed to attack the LdCT issues, such as maximum a posteriori (MAP) [16], nonlocal means (NLM) [17,18] and block-matching three-dimensional (BM3D)[19-21]. Recently, deep learning techniques were introduced as a post-processing method to solve the LdCT imaging problem [22-24]. Compared to aforementioned methods, iterative methods have full access to the sinogram information while being able to model the low dose image degrading factors [25] in the image domain, e.g. the noise [26], the finite X-ray beam etc., which is more flexible and could usually achieve better performance than its counterpart in the sinogram domain. Therefore, the iterative method can in principle obtain better image quality at the same low dosage level than the FBP. Tremendous effort has been devoted to developing sophisticated iterative methods [27-31]. Among them, Markov random field (MRF) is one of the most used prior models, which considers the local dependence between neighboring voxels. The reported MRF prior models [32-35] can suppress the streak-like artifacts as well as preserve sharp edges. Despite the success, the reported MRF prior models do not consider tissue-specific textures in the real CT images. Since tissue texture has been recognized to play an important role in detecting and characterizing lung nodules tasks, a tissue-specific MRF prior model was proposed [36-41]. While initial exploratory study on the tissue specific MRF prior model showed encouraging results, task-based evaluations are needed to demonstrate its advantages in real world tests.

In this paper, we performed an evaluation study based on two tasks of nodule detection and characterization at multiple dose levels from different mAs settings in data acquisition and variable textures from different reconstruction algorithms (the FBP, the MRF with optimized model parameters [32-35] and the tissue-specific MRF prior model [36-41]). The evaluation was performed on three dosage levels corresponding to one FdCT level and two LdCT levels for each task. The statistical hypothesis-test method was used to analyze the evaluation results between different reconstruction methods at the same dosage level.

The remainder of this paper is organized as follows. The clinical data acquisition and reconstruction strategies will be explained in the section II. The experiments and results are presented in section III. Discussion and conclusions are drawn in Section IV. Partial content of this work has been reported in the proceedings of [42].

II. Methods

2.1. Data Acquisition

133 patients with a suspicious pulmonary nodule scheduled for biopsy were recruited under informed consent and assessed prospectively. We acquired the data on a Siemens CT scanner in a spiral scanning mode. The data acquisition protocol included a setup scan at 100mAs level, a second scan at 40mAs, a third scan at 20mAs, followed by scans at either 40 or 20mAs (depending on the body size) until the needle reached the target. Kilovolt peak was fixed at 120 for all scans. The dataset of dose level 100mAs/120kVp (FdCT) was set as the reference to evaluate the performance of the other two LdCT dose levels (40/20mAs, 120kVp). Assisted by the vendor, we extracted original sinograms (line integrals) from the machine. There are 1160 views and 672 bins for each slice. The images were reconstructed to size 512×512. The three sets of sinogram (after spiral re-bin at 100, 40 and 20mAs) from each patient were then reconstructed using the following strategies.

2.2. Image Reconstruction Algorithms

As a widely used analytical method, the FBP reconstruction strategy with proper noise filtering was adapted as reference baseline. When using the FBP, “ramp” filter was used for 100mAs sinogram (FBP-R) and Hanning windowing (FBP-W) with cutoff frequency at 0.5 Nyquist frequency was applied to the 40mAs and 20mAs sinograms. The same settings were used [39] as at low dose, FBP-W yields better signal over noise ratio. We implemented FBP using the open source code Michigan image reconstruction toolbox (MIRT). The online access is [43].

One widely recognized iterative reconstruction method known as Huber MRF (MRF-H) was used serving as another reference baseline from the iterative method family. It models the fidelity term as weighted least squares and the priori term by the well-established MRF model [32-35]. This model could be mathematically formulated as:

$${\mu }^{\ast }=arg\underset{\mu }{\text{min}}\{(y-A\mu {)}^{T}D(y-A\mu )+\beta U(\mu )\},$$ (1)

where μ stands for the attenuation map (image); y denotes the acquired projection data; A is the response matrix, where each element is calculated as the intersection length of the projection ray with image pixel, T represents the transpose operation, D is a diagonal matrix, where each diagonal element represents the statistical weight for each projection ray, β is the parameter to balance the data fidelity and priori term, U(μ) is the priori term which can be expressed as the MRF model:

$$U(\mu )=\sum _j\sum _{m\in W_j}{w}_{jm}\varphi ({\mu }_j-{\mu }_m),$$ (2)

where index j runs over all the pixels in the image domain, W_j denotes a fixed neighborhood window (7 × 7 neighborhood window was selected in this paper) near by the j th image pixel, w_jm is the MRF coefficient that indicates the interaction degree between pixel j and pixel m. In this work the MRF coefficients are chosen to be inversely proportional to the Euclidean distance between two neighboring pixels, as often used in previous literature. In the 2D case with a 7 × 7 window, the weights are then given by:

$$\left[\begin{array}{ccccccc}\hfill 0.011\hfill & \hfill 0.013\hfill & \hfill 0.015\hfill & \hfill 0.016\hfill & \hfill 0.015\hfill & \hfill 0.013\hfill & \hfill 0.011\hfill \\ \hfill 0.013\hfill & \hfill 0.017\hfill & \hfill 0.022\hfill & \hfill 0.024\hfill & \hfill 0.022\hfill & \hfill 0.017\hfill & \hfill 0.013\hfill \\ \hfill 0.015\hfill & \hfill 0.022\hfill & \hfill 0.034\hfill & \hfill 0.048\hfill & \hfill 0.034\hfill & \hfill 0.022\hfill & \hfill 0.015\hfill \\ \hfill 0.016\hfill & \hfill 0.024\hfill & \hfill 0.048\hfill & \hfill 0\hfill & \hfill 0.048\hfill & \hfill 0.024\hfill & \hfill 0.016\hfill \\ \hfill 0.015\hfill & \hfill 0.022\hfill & \hfill 0.034\hfill & \hfill 0.048\hfill & \hfill 0.034\hfill & \hfill 0.022\hfill & \hfill 0.015\hfill \\ \hfill 0.013\hfill & \hfill 0.017\hfill & \hfill 0.022\hfill & \hfill 0.024\hfill & \hfill 0.022\hfill & \hfill 0.017\hfill & \hfill 0.013\hfill \\ \hfill 0.011\hfill & \hfill 0.013\hfill & \hfill 0.015\hfill & \hfill 0.016\hfill & \hfill 0.015\hfill & \hfill 0.013\hfill & \hfill 0.011\hfill \end{array}\right].$$ (3)

For MRF-H, ϕ is the Huber function, which is defined as:

$$\varphi (\Delta )=\{\begin{array}{cc}{\Delta }^2\hfill & \mid \Delta \mid \le \delta \hfill \\ 2\delta \mid \Delta \mid -{\delta }^2\hfill & \mid \Delta \mid >\delta \hfill \end{array}\phantom{\}},$$ (4)

where δ is an adjustable parameter to balance the desired regional smoothness and sharp edges.

In our previous works [36-41], we proposed an iterative reconstruction method, the MRF-T, accounting for tissue-specific texture priori to achieve piecewise texture preservation. This method takes advantage of the MRF theory’s description of the neighbor configuration for the clinically desired task of preserving the tissue-specific tissue textures in the reconstructed LdCT images. Different from the regional noise smoothing penalty in Eq. (2), we learnt the MRF coefficients from the tissue-specific region of the previous full-dose diagnostic quality CT images. In other words, w_jm in Eq. (2) was replaced by the tissue specific MRF coefficients w_r, which can be learnt by solving the following least squares problem:

$${\mathit{w}}_r^{FD}=arg\underset{{\mathit{w}}_r}{\text{min}}\sum _{k\in Region(r)}{\left(u_k^{FD}-{\mathit{w}}_r^T{\mathit{u}}_{{\Omega }_k}^{FD}\right)}^2,$$ (5)

where the index r runs through all the tissue-specific regions, such as lung, fat, muscle and bone. Vector μ^FD is the full-dose CT image (from FBP-100), Ω denotes the neighborhood window (7 × 7 neighborhood window was selected in this paper). This strategy incorporates the tissue-specific textures of lung, fat, muscle and bone from the previous full-dose diagnostic quality CT images as the prior knowledge for the Bayesian (or posteriori) reconstruction of current LdCT images. Tissue segmentation is performed by the Vector Quantization method based on an initialization results from FBP [44], refer to the MRF-T algorithm. One example of MRF-T for lung is shown below.

$$\left[\begin{array}{ccccccc}\hfill -0.051\hfill & \hfill 0.099\hfill & \hfill -0.021\hfill & \hfill -0.074\hfill & \hfill -0.012\hfill & \hfill 0.092\hfill & \hfill -0.034\hfill \\ \hfill 0.085\hfill & \hfill -0.114\hfill & \hfill -0.053\hfill & \hfill 0.065\hfill & \hfill -0.044\hfill & \hfill -0.117\hfill & \hfill 0.059\hfill \\ \hfill 0.001\hfill & \hfill -0.135\hfill & \hfill 0.103\hfill & \hfill 0.288\hfill & \hfill 0.135\hfill & \hfill -0.146\hfill & \hfill 0.023\hfill \\ \hfill -0.049\hfill & \hfill 0.167\hfill & \hfill 0.206\hfill & \hfill 0\hfill & \hfill 0.207\hfill & \hfill 0.170\hfill & \hfill -0.052\hfill \\ \hfill 0.025\hfill & \hfill -0.146\hfill & \hfill 0.134\hfill & \hfill 0.288\hfill & \hfill 0.105\hfill & \hfill -0.141\hfill & \hfill 0.007\hfill \\ \hfill 0.055\hfill & \hfill -0.114\hfill & \hfill -0.041\hfill & \hfill 0.061\hfill & \hfill -0.050\hfill & \hfill -0.114\hfill & \hfill 0.084\hfill \\ \hfill -0.033\hfill & \hfill 0.090\hfill & \hfill -0.009\hfill & \hfill -0.073\hfill & \hfill -0.001\hfill & \hfill 0.100\hfill & \hfill -0.053\hfill \end{array}\right].$$ (6)

One major difference between MRF-T and MRF-H is that MRF-H does not consider the tissue inhomogeneity across the FOV and uses the same MRF weights for all tissue regions through the whole image volume. The newly reported MRF-T method not only considers the tissue inhomogeneity across the FOV but also accounts for the tissue-specific nature of textures reflected in the derived tissue-specific MRF weights for each tissue type. More details of the MRF-T weights can be found in [39]. The pseudo code of the MRF-T is presented below, where r denotes the residual between sinogram and estimation, σ_e denotes the variance of electronic noise, and N_i⁰ denotes the incident flux of ith ray. The other annotations have the same meaning in the previous definition. More details of the MRT-weights and the reconstruction algorithm can be found in [39]. This pseudo-code almost applies for the MRF-H implementation but with constant MRF weights.

Algorithm of MRF-T

$$\begin{array}{cc}\hfill & \#\text{Initialization:}\hfill \\ \hfill & \mu =FBP\{\mathit{y}\};\mathit{q}=\mathbf{A}\mu ;\mathit{r}=\mathit{y}-\mathit{q};\hfill \\ \hfill & \mathbf{D}=diag\left\{\frac{(N_i^o{e}^{-q_i}{)}^2}{N_i^o{e}^{-q_i}+{\sigma }_e^2}\right\}\hfill \\ \hfill & {\lambda }_j={\mathbf{A}}_j^T\mathbf{D}{\mathbf{A}}_j,\forall j\hfill \\ \hfill & \#\text{For each iteration:}\hfill \\ \hfill & \text{Begin}\hfill \\ \hfill & \text{For each voxel j:}\text{determine tissue region for voxel j},{}_{j\in Region(r)}\hfill \\ \hfill & \text{choose corresponding MRF weight set}\hfill \\ \hfill & \text{begin}\hfill \\ \hfill & {\mu }_j^{old}≔{\mu }_j\hfill \\ \hfill & {\mu }_j^{new}≔\frac{{\mathbf{A}}_j^T\mathbf{D}\mathit{r}+{\lambda }_j{\mu }_j^{old}+\beta \sum _{m\in {\Omega }_j}{w}_{jm}^{FD}{\mu }_m}{{\lambda }_j+\beta \sum _{m\in {\Omega }_j}{w}_{jm}^{FD}}\hfill \\ \hfill & {\mu }_j≔\max \{0,{\mu }_j^{new}\}\hfill \\ \hfill & \mathit{r}≔\mathit{r}+{\mathbf{A}}_j({\mu }_j^{old}-{\mu }_j)\hfill \\ \hfill & \text{end}\hfill \\ \hfill & \mathbf{D}≔diag\left\{\frac{(N_i^o{e}^{-{\sum }_j{\mathrm{A}}_{ij}{\mu }_j}{)}^2}{N_i^o{e}^{-{\sum }_j{\mathrm{A}}_{ij}{\mu }_j}+{\sigma }_e^2}\right\}\hfill \\ \hfill & {\lambda }_j≔{\mathbf{A}}_j^T\mathbf{D}{\mathbf{A}}_j,\forall j\hfill \\ \hfill & \text{End}\hfill \end{array}$$

The above three CT reconstruction methods, FBP (including FBP-R and FBP-W), MRF-H and MRF-T, were implemented to reconstruct the acquired three dose level sinograms respectively. The three reconstruction algorithms deal with the noise and prior knowledge in different ways and are expected to have different tissue textures in their reconstructed images. Furthermore, the textures will also be affected by the dose level for the same reconstructed method. In the following sections, we report our investigations on the dose and textures across the images reconstructed by the three mentioned algorithms for the two clinical tasks of (1) lung nodule localization or detection and (2) nodule characterization.

III. Experimental design and results

3.1. Experiment Design

Following the description in section II, the acquired three dose level sinograms of the 133 subjects were reconstructed by various strategies, FBP-R for 100mAs, FBP-W, MRF-H and MRF-T for 40 and 20mAs. To make the annotation simple, each case was denoted as algorithm-dose. For example, FBP-W-40 means the image is reconstructed by FBP-W and its sinogram is acquired at 40mAs. Then experienced thoracic radiologists reviewed all the reconstructed images randomly, blinded to the image dose level and the algorithm used for the reconstructions.

For each dose level dataset, all the nodules identified in the image volume were marked, including the 133 biopsy target nodules and 66 other non-target nodules. These 66 non-target nodules were not recommended for biopsy in the patients who were scheduled for the medical intervention operations. The analysis of these nodules in this paper focuses on: a) the characterization of the 133 nodules recommended for biopsy, and b) the detection of the 199 total nodules with each reconstruction method.

One experienced radiologist scored the images of the 133 target nodules. The score quantified how confident he was in characterizing the nodules. Usually, an image with more details of textures and less artifacts tend to have a higher score. For detection task, two radiologists viewed all images including target and non-target nodules. They localized suspicious lung nodules and their sizes independently. Then they discussed and confirmed all detected nodules. Similar to the scoring, it is expected that more nodules can be detected in the images with better texture preservation and less artifacts. The scoring and detection results will be presented in detail in the following section.

3.2. Nodule Characterization

Figure 1 compares the reconstructed images of the same patient at the three dosage levels. The 100mAs FBP image is treated as the reference baseline, where the nodule can be clearly detected and characterized. For the LdCT at both the 40mAs and 20mAs, the images reconstructed by FBP are overall blurred, in which the structure of capillaries cannot be seen clearly. In the images reconstructed by MRF-H, the nodule edge is sharp and has high contrast with its neighboring pixels, while the details inside the nodules are over smoothed. The MRF-T images overcome the blur issue and preserve the nodule details, which do not look significantly different from the reference baseline.

Fig. 1:

Comparison between the full dose CT image (100mAs) and the low dose image (40mAs and 20mAs) reconstructed using different algorithms.

A 10-point Likert scale was used for all scoring to characterize the 133 target nodule images according to the criteria of malignancy described in [45,46]. Each of the 133 nodule volume images has 7 scores:

1. One score from FBP-R at dose level of 100mAs;

2. Two scores from FBP-W reconstructions at two dose levels of 40 and 20mAs respectively;

3. Two scores from MRF-H reconstructions at two dose levels of 40 and 20mAs respectively;

4. Two scores from MRF-T reconstructions at two dose levels of 40 and 20mAs respectively.

The scoring results are plotted in Fig. 2. For each nodule, all the scores of the same reconstruction method are shown by light colors in the background, whose starting point is always the score of the FBP-R-100. The three thicker lines link the mean scores of all the nodules for each reconstruction method with the bars representing the standard deviation at the three dose levels. The colors of black, blue and red are in according with FBP-W, MRF-H, MRF-T methods. In our experience, at full dose (100 mAs), the signal over background ratio was so good that the better noise modelling of the iterative methods would not produce much benefit while the computational cost is much higher than analytical methods. In this paper, as we are focusing low dose reconstruction, the full dose base line was only reconstructed by FBP and serves as common start point of the three curves.

Fig. 2:

Scoring results on characterization of the target nodule images. Each line in the background denotes scores on one subject using different method. Each line in the foreground denotes the mean/std. dev. of each method for all 133 subjects. Note that the FBP-R-100 results were used as common baseline for all 3 methods at 100mAs.

Clearly lower dose levels yield lower image characterization scores implying lower image quality. At low dose, among these three curves, the MRF-T registered highest average score followed by the MRF-H then the FBP-Hann. These results agree with our expectation. Firstly, the SIR methods (MRF-H and MRF-T) account for more accurate noise model at image domain while the analytical FBP method can only suppress specific noise spectrum at spatial frequency domain. Secondly, the MRF-T method considers the tissue-specific textures from previous full-dose high-quality diagnostic CT or FdCT scans as the a priori knowledge and applies the knowledge for tissue-specific regional adaptive reconstruction of the current LdCT images. The consideration of tissue-specific textures from previous FdCT scans is expected to enhance the textures in the reconstructed LdCT images. Note that lesion heterogeneity is a critical attribute or indication of malignance [38]. Image texture has been shown to be a critical metric to characterize the heterogeneity and has also been recognized as an imaging biomarker [38,47]. Thus, it is anticipated that experienced thoracic radiologists shall assess the MRF-T reconstructions with higher scores on nodule characterization. This expectation is further realized in another task-based image evaluation on the detection of nodules (to be reported in the next section).

In addition to visualizing the scores in Fig. 2, we further compared the three reconstruction methods using statistical analysis. In the analysis, linear mixed effect model for repeated measurements was used, where each set of the volume images was treated as a random effect. This analysis was performed using SAS 9.4 (SAS Institute Inc., Cary NC).

Table 1 presents the difference of the mean scores between the test algorithm and the FBP-R-100, i.e. E(FBP-R-100) - E(test) and the corresponding confidence intervals (CI) (the third and fourth columns). MRF-T producing the smallest differences at 40 and 20 mAs indicates its superior performance over the FBP-W and MRF-H. We also performed hypothesis testing for each method against the baseline FBP-R-100 with them yielding same scores as the null hypothesis. The p-values are shown in the last column of Table 1. It is observed that only MRF-T-40 has a large enough p-value (>5%) that the null hypothesis could not be rejected, i.e. we could not tell whether the MRF-T-40 yield same score as the baseline FBP-R-100.

Table 1:

Statistical analysis of score difference comparing with reference baseline FBP-100. This analysis was performed using SAS 9.4 (SAS Institute Inc., Cary NC).

Method	Score mean difference	Lower Limit of 95% CI	Upper Limit of 95% CI	P-value
FBP-40	3.33	3.03	3.63	<.0001
FBP-20	4.39	4.09	4.69	<.0001
MRF-H-40	1.71	1.41	2.00	<.0001
MRF-H-20	2.17	1.87	2.47	<.0001
MRF-T-40	0.26	−0.04	0.55	0.0884
MRF-T-20	0.73	0.43	1.02	0.0002

We also performed hypothesis tests for mean score difference between pairs of algorithms and doses. The null hypothesis is each algorithm-dose pair yields the same score. The p-values are shown in Table 2. For the same reconstruction method between different dose levels, there was no strong evidence that MRF-H-40 and MRF-H-20 (red in Table 2) yields different score with p-value = 0.0879 > 0.05 (similarly, for MRF-T-40 and MRF-T-20). This was not the case for the FBP-W-40 and FBP-W-20. This observation indicates the SIR methods (MRF-H and MRF-T) are less sensitive to the dose variation than analytical FBP-W method. Between different reconstruction methods, it was strongly indicated that all 3 methods yield different scores at same dose from the very small p-value (<<0.05).

Table 2:

P-values of pairwise comparison in characterizing target nodules among three algorithms.

Method	MRF-H-40	MRF-T-40	FBP-W-20	MRF-H-20	MRF-T-20
FBP-W-40	<0.0001	<0.0001	<0.0001	<0.0001	<0.0001
MRF-H-40	-	<0.0001	<0.0001	0.0879	3.00E-04
MRF-T-40	-	-	<0.0001	<0.0001	0.0759
FBP-W-20	-	-	-	<0.0001	<0.0001
MRF-H-20	-	-	-	-	<0.0001

In Table 3, we summarized the image mean score difference between algorithm-dose pairs along with its 95% CI for another pairwise comparison. Considering the fluctuation when radiologist scored the same image at different time, we assumed that a score difference larger than 3 implies a meaningful difference (in yellow) and that smaller than 1.5 implies no meaningful difference (in blue). The in-between pairs are painted in pink. Under this convention, MRF-T-40 and MRF-T-20 has a meaningful difference with FBP-40 and FBP-W-20. However, MRF-H-40 only has a meaningful difference with FBP-W-20. MRF-H-20 has no meaningful difference with FBP-W-40. This indicates the image quality of MRF-T-20 is better than that of MRF-H-20 and FBP-W-40. The image quality of MRF-H-20 and FBP-W-40 is similar.

Table 3:

Pairwise score difference in characterizing target nodules along with its 95% confidence intervals (CI).

Method	MRF-H- 40	MRF-T- 40	FBP-W-20	MRF-H-20	MRF-T-20
FBP-W-40	1.63 (1.17,2.08)	3.07 (2.63,3.52)	−1.06 (−1.46, −0.66)	1.16 (0.69,1.63)	2.6 (2.14,3.06)
MRF-H-40	-	1.45 (0.94,1.96)	−2.68 (−3.16, −2.21)	−0.46 (−1,0.07)	0.98 (0.45,1.5)
MRF-T-40	-	-	−4.13 (−4.6, −3.66)	−1.91 (−2.44, −1.38)	−0.47 (−0.99,0.05)
FBP-W-20	-	-	-	2.22 (1.73,2.71)	3.66 (3.18,4.15)
MRF-H-20	-	-	-	-	1.44 (0.9,1.98)

There is no meaningful difference between 40mAs and 20mAs for FBP-W, MRF-H and MRF-T reconstruction methods (painted in blue). This implies that we can reduce the dose from 40mAs level to 20mAs level without meaningful difference for each specific reconstruction method. One possible reason could be that the noise below 40mAs degraded the image texture to a degree that the texture is less sensitive to the dose. It also implies the image texture below 40mAs may not be quite useful for nodule characterization.

Based on the statistical analysis, only the MRF-T-40 performed without any significant difference with the FBP-R-100. We demonstrated more cases of the nodules in Fig. 4 for detailed visual judgement comparing with the reference baseline FBP-R-100. The first case is one ground-glass type nodule. The glass-like structure is an important indicator for high chance to be cancer and is well preserved in the MRF-T-40. In the second case, the nodule is near the wall, where the nodule edge and surrounding details in MRF-T-40 are similar with that in FBP-R-100. For the other cases in Fig. 3, the MRF-T-40 images also do not look significantly different with the FBP-R-100. It indicates we can use the MRF-T method in follow-up CT scans to reduce total radiation dose when previous full dose texture information was available. When this information is not available, we demonstrated a texture database from full dose scans could also provide promising results for a patient, who has no scan in the database [41].

Fig. 4:

Detection rate for three groups of nodules among different reconstruction methods. 95% Clopper-Pearson exact CIs are shown as bars.

Fig. 3:

Comparison between the full dose CT image (upper, 100mAs) and the low dose image (lower, 40mAs) reconstructed using MRF-T method.

3.3. Nodule Detection

A lung nodule is a small, round or irregular growth of tissue within the chest cavity. Nodules are generally considered to be less than 30mm in size, as larger growths are called masses and are presumed to be malignant. Nodules between 5-30mm may be benign or malignant, with the likelihood of malignancy increasing with size. Detecting lung nodules as early as possible is useful to decrease the incidence rate. Early detection requires the ability to detect nodules as small as 3mm.

In nodule detection task, the experienced thoracic radiologists were asked to detect not only the 133 biopsy target nodules (10mm to 30 mm) but also 66 other non-target nodules (3mm to 10mm). An experienced radiologist viewed all images and detected suspicious nodules (Nsus) first. Then from those suspicious nodules two radiologists confirmed those more likely real nodules (Nconf) combining all images for the same patient together with other diagnostic reports. The total number of confirmed nodules, Nconf_total, is defined as Nconf from all methods listed in Table 4 (duplications only count once). We counted the number of missed confirmed nodules using individual method with regarding to Nconf_total. Results are listed in Table 4. There are a lot of factors that may affect the detection rate, like the image spatial resolution, noise, contrast etc. This work mainly studied the effect of texture as a task-based evaluation of the MRF-T algorithm.

Table 4:

Nodule detection rates with their 95% CIs by different reconstruction methods.

Method	Target nodules only (N=133)		Non-target nodules only (N=66)
	# of missed nodule	Detection rate with 95% CI	# of missed nodule	Detection rate with 95% CI
FBP-R-100	0	1.0000 (0.9726, 1.0000)	11	0.8333 (0.7213, 0.9138)
FBP-W-40	1	0.9925 (0.9588, 0.9998)	25	0.6212 (0.4934, 0.7378)
FBP-W-20	4	0.9699 (0.9248, 0.9917)	27	0.5909 (0.4629, 0.7105)
MRF-H-40	0	1.0000 (0.9726, 1.0000)	22	0.6667 (0.5399, 0.7780)
MRF-H-20	3	0.9774 (0.9355,0.9953)	22	0.6667 (0.5399, 0.7780)
MRF-T-40	0	1.0000 (0.9726 ,1.0000)	15	0.7727 (0.6530, 0.8669)
MRF-T-20	2	0.9850 (0.9467, 0.9982)	16	0.7576 (0.6364 ,0.8546)

^*95% CIs were Clopper-Pearson exact CIs.

The detected nodule numbers and its detection rate with 95% CI are shown in Table 4. We compared the detection rate for only target nodules, only non-target nodules. For the target nodules, all of them were found in the images of FBP-R-100, MRF-T-40, MRF-H-40, i.e. the missed nodules were zero. It implies the radiation can be reduced by 3/5 using the MRF-T method when previous full dose texture available (e.g. follow up scans). For the non-target nodules, the detection rate of FdCT was ~0.80. The detection rate of LdCT is above 0.75 by MRF-T, but below 0.68 and 0.62 by MRF-H and FBP respectively. The experimental results of all the three group nodules show better performance of MRF-T at low dose levels.

To make more intuitive comparison, the detection rates for the target nodules and non-target nodules are bar plotted in Fig. 4 with its corresponding two bounds of 95% CI. In Fig. 4, the MRF-T method outperforms the other two methods at the same dosage level and performs the most similar with the reference FBP-R-100. Comparing the pictures in Fig. 4, all the methods and dosage levels are less different for the target nodule group and more different for the non-target nodule group. Figure 4 demonstrated MRF-T method could achieve higher detection rate than the FBP-Hann and MRF-H at low dose.

Similar to the nodule characterization, we also performed hypothesis tests for pairwise comparison among the 7 algorithm-dose combinations for the detection task. The null hypothesis is each pair of the algorithm-dose yields same detection rate. P-values were based on McNemar’s test with exact p-values from binomial distribution. The results are shown in Table 5. All the p-values with no strong evidence to reject null hypothesis (>0.05) are highlighted in Table 5.

Table 5:

Pairwise comparison in detecting all nodules among three algorithms at three dose levels. P-values were based on McNemar’s test with exact p-values from binomial distribution.

	FBP- W-40	MRF- H-40	MRF- T-40	FBP- W-20	MRF- H-20	MRF- T-20
FBP-R-100	0.0007	0.0433	0.5034	<0.0001	0.0043	0.1435
FBP-W-40	-	0.5034	0.0192	0.3593	1.0000	0.1516
MRF-H-40	-	-	0.0156	0.1360	0.6900	0.5572
MRF-T-40	-	-	-	0.0037	0.0755	0.6776
FBP-W-20	-	-	-	-	0.2101	0.0023
MRF-H-20	-	-	-	-	-	0.0156
MRF-T-20	-	-	-	-	-	-

For the same reconstruction method between different dose levels, there is no statistically significant difference between MRF-H-40 and MRF-H-20, between MRF-T-40 and MRF-T-20, between FBP-W-40 and FBP-W-20, with p-value 0.69, 0.6776, 0.3593 respectively. This observation is different from that for characterization task. For the characterization task, only the two SIR methods showed no significant difference. For the detection task, the FBP method also shows no significant difference. It implies that the characterization task is more sensitive to the textures compared to the detection task, which requires more dose or more enhanced textures by the reconstruction algorithm. This may explain the differences between Table 2 and Table 5 for the same pairs. Between different reconstruction methods, MRF-T-40 and MRF-T-20 showed no statistically significant difference from FBP-R-100 (p-values = 0.5034 and 0.1435), while both MRF-H and FBP at low dose performed differently from FBP-R-100 (all p-values < 0.05). According to Table 5, MRF-T-20 performed similarly as FBP-100 with only 20% radiation dose.

IV. VI Discussion and Conclusion

In this study, dose and textures were investigated across CT images reconstructed by two well-known spatially invariant CT image reconstruction strategies and one spatially-variant a priori tissue-specific regional texture MRF-T model for lung nodule localization and characterization at three dose levels of 100mAs, 40mAs and 20mAs.

Both the spatially invariant algorithms of (analytical) FBP (by spatially invariant filtration across the FOV regardless different tissue regions inside the FOV) and (statistical) MRF-H model (by spatially invariant Huber weights or matrix across the FOV regardless different tissue regions inside the FOV) focus more on the noise reduction. MRF-T model takes tissue-specific texture from the previous FdCT as the prior knowledge and focuses more on the texture preservation. Our previous work demonstrated the enhancement of texture reconstruction using the MRF-T for low dose (20mAs) scans [39]. In this paper, we performed extensive tests (133 subjects × 3 dosages × 3 methods) to investigate the impact of the MRF-T algorithm on real-world tasks of nodule detection and characterization. Nodule detection results (Fig. 4 and Table 4) and characterization scores (Fig. 2 and Table 1) showed the MRF-T algorithm outperformed the MRF-H and FBP-Hann at lower dosage.

One caveat of the MRF-T introduced in this paper is full dose scan needs to be done at least once to provide accurate texture information. To release this limitation and expand application of MRF-T, we proposed building an MRF coefficient database to assist low dose CT scans without a previous full dose prior, the MRF-T-DB method [41]. In [41], we demonstrated the reconstructed tissue textures could be largely enhanced (higher fidelity with regarding to full dose textures) using MRF coefficients from another subject from the database. And preliminary results of matching one proper texture prior from database using physiological and other factors are reported in [48]. In addition to this radiologist scoring evaluation, we are also investigating impact of the MRF-T results on downstream detection/diagnose algorithms [47, 49]. This automated task-based evaluation is one of our future research interests.

In summary, we reconstructed 399 CT scans at lower dose (40 and 20mAs) with the FBP-W, the MRF-H and the proposed MRF-T algorithms. Based on the reconstructed images, nodule detection and characterization tasks were performed by experienced radiologists. The MRF-T algorithm showed advantages in both tasks than the other two. To relief the requirement of an existing previous full dose scan, in the future we will investigate the use of a database as in our previously proposed MRF-T-DB algorithm [41,48].